bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

1 Title: Neuroanatomical Norms in the UK Biobank: The Impact of Allometric Scaling, Sex and

2 Age.

3 Running title: Neuroanatomical Norms in the UK Biobank

4 Authors: Camille Michèle Williams1*, Hugo Peyre1,2,3, Roberto Toro4,5,6, & Franck Ramus1.

5 1. Laboratoire de Sciences Cognitives et Psycholinguistique, Département d'Etudes

6 Cognitives, École Normale Supérieure, EHESS, CNRS, PSL University, 75005, Paris,

7 France

8 2. INSERM UMR 1141, Paris Diderot University, Paris, France.

9 3. Department of Child and Adolescent Psychiatry, Robert Debré Hospital, APHP, Paris,

10 France.

11 4. Human Genetics and Cognitive Functions, Institut Pasteur, UMR 3571 CNRS

12 5. Center for Research and Interdisciplinarity (CRI), INSERM U1284

13 6. Université de Paris, Paris, France.

14 *CORRESPONDING AUTHOR: Camille Michèle Williams, LSCP, Département d’Etudes

15 Cognitives, École Normale Supérieure, 29 rue d'Ulm, 75005 Paris, France. Email:

16 [email protected].

17

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 1 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

18 Table of Contents 19 Abstract ...... 4 20 1. Introduction ...... 7 21 2. Methods ...... 9 22 2.1. Participants ...... 9 23 2.1.1. Brain Image Acquisition and Processing...... 9 24 2.1.2. Total Brain Volume (TBV) ...... 9 25 2.1.3. Scanner Site ...... 9 26 2.1.4. Sex ...... 10 27 2.1.5. Age ...... 10 28 2.2. Image Derived-Phenotypes (IDPs) ...... 10 29 2.2.1. Global IDPs ...... 10 30 2.2.2. Regional IDPs ...... 11 31 2.3. Statistical Analyses ...... 11 32 2.3.1 Data Transformation...... 12 33 2.3.2. Analyses...... 12 34 2.3.3. Global Analyses...... 12 35 2.3.4 Regional Analyses...... 13 36 2.3.5 Person-level Neuroanatomical Markers...... 13 37 2.3.6 Person-level Global Neuroanatomical Deviance...... 13 38 2.3.7 Exploratory Analyses...... 14 39 2.3.8 Multiple Comparison Corrections...... 14 40 3. Results and Discussion ...... 16 41 3.1 Allometry ...... 16 42 3.1.1 Global Allometry ...... 16 43 3.1.2 Cortical Allometry ...... 17 44 3.1.3 Subcortical Allometry ...... 19 45 3.1.4 Mean Thickness and Surface Area Scaling with TBV ...... 19 46 3.1.5 Sex or Age-Dependent Allometry ...... 20 47 3.1.6 Conclusion on Allometry ...... 20 48 3.2 Sex differences...... 22 49 3.2.1 Global Measures ...... 22 50 3.2.2. Total Cerebellar GMV ...... 22 51 3.2.3 Regional Cerebellar GMV ...... 22 52 3.2.4 Whole Subcortical Volumes ...... 23 53 3.2.5 Subcortical Subsegmentations ...... 24 54 3.2.6 Cortical Regions ...... 25 55 3.2.7 Sex differences in variance ...... 28 56 3.2.8 Conclusion on sex differences ...... 30 57 3.3 Age Effects ...... 30 58 3.3.1 Global Measures ...... 30 59 3.3.2 Cerebellar Volumes ...... 31 60 3.3.3 Whole Subcortical and Subcortical Subsegmentation Volumes ...... 31 61 3.3.4 Cortical regions ...... 32 62 3.3.5 Conclusion of Age Effects ...... 35 Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 2 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

63 3.4. Does Brain Allometry Influence Reported Results? ...... 35 64 3.5 Neuroanatomical Norms ...... 36 65 3.6 Limitations ...... 41 66 4. Conclusion...... 42 67 5. References ...... 43 68 69

70

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 3 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

71 Abstract

72 Few neuroimaging studies are sufficiently large to adequately describe population-wide 73 variations. This study’s primary aim was to generate neuroanatomical norms and individual 74 markers that consider age, sex, and brain size, from 629 cerebral measures in the UK Biobank (N 75 = 40 028). The secondary aim was to examine the effects and interactions of sex, age, and brain 76 allometry – the non-linear scaling relationship between a region and brain size (e.g., Total Brain 77 Volume) across cerebral measures. 78 Allometry was a common property of brain volumes, thicknesses, and surface areas (83%) 79 and was largely stable across age and sex. Sex differences occurred in 67% of cerebral measures 80 (median |β|= 0.13): 37% of regions were larger in males and 30% in females. Brain measures 81 (49%) generally decreased with age, although aging effects varied across regions and sexes. While 82 models with an allometric or linear covariate adjustment for brain size yielded similar significant 83 effects, omitting brain allometry influenced reported sex differences in variance.

84 This large scale-study advances our understanding of age, sex, and brain allometry’s 85 impact on brain structure and provides data for future UK Biobank studies to identify the cerebral 86 regions that covary with specific phenotypes, independently of sex, age, and brain size.

87

88

89 Word count: 200 90 91 92

93 94 95 96

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 4 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

97 Graphical Abstract

98

99

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 5 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

100 Keywords 101 Cerebral Norms, Brain Volumes, Cortical Thickness, Cortical Surface Area, Allometry, Sex 102 Differences

103 Highlights 104 • We created neuroanatomical norms and individual markers for the UK Biobank (N=40 105 028) 106 • Allometry was common across 83% of brain volumes, thicknesses, and surface areas 107 • 67% of regions differed between sexes: 37% were larger in males and 30% in females 108 • Omitting brain allometry influenced reported sex differences in variance 109 • 49% of regions declined with age, with variations across regions and sexes 110 111 Acknowledgements 112 This work received support under the program “Investissements d’Avenir” launched by the French 113 Government and implemented by ANR with the references ANR-17-EURE-0017 and ANR-10- 114 IDEX-0001-02 PSL. Funding was also obtained from Fondation pour l'Audition (FPA RD-2016- 115 8 research grant). This research has been conducted using the UK Biobank Resource. Declarations 116 of interest: none. 117 118 Conflict of interest 119 On behalf of all authors, the corresponding author states that there is no conflict of interest. 120 121 Data/Code Availability 122 This research has been conducted using data from UK Biobank, a major biomedical database 123 (http://www.ukbiobank.ac.uk/). Restrictions apply to the availability of these data, which were 124 used under license for this study: application 46007. Preregistration and code are available on OSF: 125 https://osf.io/s4qc5/?view_only=bb067d96d0df4ae4902f99747d60e828. 126

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 6 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

127 1. Introduction 128 Although all humans share a common brain structure and organization, they also vary in 129 terms of the size and shape of their brain and its subcomponents. These neuroanatomical variations 130 are thought to partly underlie differences in cognitive and behavioral traits and in the risk of 131 developing psychiatric and neurological disorders (for review Dallaire-Théroux et al., 2017; 132 Deary, 2010; Jumah et al., 2016; Oakes et al., 2017; Schmidt et al., 2018). Yet, most of these 133 studies rely on relatively small samples and suffer from high sampling variability. When the 134 sample is too small to accurately represent the control or target population, spurious 135 neuroanatomical markers may be reported. Moreover, if true effects are observed in small samples, 136 their size would be exaggerated as only large effects would pass a conventional statistical 137 significance threshold (e.g., p < 0.05) with few degrees of freedom (for review Szucs & Ioannidis, 138 2017, 2020). Thus, despite hundreds of studies, few neuroanatomical measures can be declared as 139 robust markers of cognitive traits or psychiatric and neurological disorders (Gong et al., 2019; 140 Marek et al., 2020; Matsuo et al., 2019; Peyre et al., 2020; Ramus et al., 2018; Williams et al., 141 2020). 142 An alternative approach to comparing clinical and healthy groups would be to compare 143 clinical groups with population norms, as is done with well-established cognitive dimensions, such 144 as general intelligence, personality, and psychopathology scales (Beck et al., 1996; Costa Jr. & 145 McCrae, 2008; Wechsler et al., 2008). If neuroanatomical norms for a population were available, 146 then comparing any clinical group to these norms would overcome the issue of sampling variability 147 in the control group. However, neuroanatomical norms are not easy to establish, as they require 148 large populations, and neuroanatomical measures often depend on MRI scanner characteristics and 149 acquisition sequences. Valid norms would therefore only be established within a given study in a 150 single scanner, or in a small set of comparable scanning sites with similar acquisition protocols as 151 done by the UK Biobank. 152 For this reason, the UK Biobank, the largest neuroimaging dataset available to date (N ~ 153 40 000), is an ideal candidate to create neuroanatomical norms that could be re-used for multiple 154 studies of neurological and psychiatric disorders. These norms should be sex-specific , given that 155 the two sexes differ on a number of neuroanatomical brain measures (Kaczkurkin et al., 2019; 156 Lotze et al., 2019; Ritchie et al., 2018; Ruigrok et al., 2014; Sanchis-Segura et al., 2019), and have 157 different risks of developing certain neurological and psychiatric disorders (Beam et al., 2018; Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 7 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

158 Boyd et al., 2015; Seedat et al., 2009). And age should also be considered, as it is associated with 159 variations in neuroanatomical measures (Fjell et al., 2013; Hurtz et al., 2014; Narvacan et al., 2017; 160 Vinke et al., 2018; Wierenga et al., 2014), cognitive function (Simon R. Cox et al., 2018; S.R. Cox 161 et al., 2019), and disease risk (Fiske et al., 2009; Fjell et al., 2009; Jellinger & Attems, 2015). 162 Finally, global brain measures should be taken into account to create norms that are 163 independent of variations in brain size. Although there is mounting evidence that brain allometry 164 - the non-linear scaling relationship between regional and global brain dimensions - is an inherent 165 property of the brain (Finlay et al., 2001; Jäncke et al., 2015a; Liu et al., 2014; Mankiw et al., 166 2017; Reardon et al., 2018; Toro et al., 2009; Williams et al., 2020), standard modes of adjustment 167 for individual differences in global measures, such as the proportion method, or linear covariate 168 adjustment, omit brain allometry. To this day, numerous studies have shown that different methods 169 of adjustment for brain size contribute to the variability of reported volumetric group differences 170 (Lefebvre et al., 2015; O’Brien et al., 2006, 2011; Reardon et al., 2016; Sanchis-Segura et al., 171 2019) and some specifically suggest that omitting brain allometry leads to spurious group 172 differences (Mankiw et al., 2017; Reardon et al., 2016; Williams et al., 2020). Since 173 regional/global relationships follow a power function in a majority of regions, it is recommended 174 to log-transform regional and Total Cerebral Measures (TCMs; i.e., Total Brain Volume (TBV), 175 Total Mean Cortical Thickness (MCT), or Total Surface Area (TSA)) to account for allometric 176 scaling and obtain a more accurate description of the relationship between brain regions and 177 TCMs. 178 Thus, the present study’s first aim is to produced neuroanatomical norms in the UK 179 Biobank that take into account sex, age, and the allometric relationships between regional and 180 global brain measures. Our second goal is to investigate the extent to which neuroanatomical 181 variations depend on sex, age (linear and quadratic), and brain allometry effects and their 182 interactions. Finally, our third aim is to compare TCM adjustment techniques to examine whether 183 omitting brain allometry systematically biases reported results. By generating neuroanatomical 184 markers across volumes, mean thicknesses, and surface areas available in the UK Biobank, the 185 present paper provides UK population norms for future studies that aim to link regional 186 neuroanatomical markers to specific cognitive and behavioral traits or neurological and psychiatric 187 disorders. 188 Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 8 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

189 2. Methods

190 2.1. Participants 191 Participants were drawn from the UK Biobank, an open-access large prospective study with 192 phenotypic, genotypic, and neuroimaging data from 500 000 participants recruited between 2006 193 and 2011 at 40 to 69 years old in Great Britain (Sudlow et al., 2015). All participants provided 194 informed consent (“Resources tab” at https://biobank.ctsu.ox.ac.uk/crystal/field.cgi?id=200). The 195 UK Biobank received ethical approval from the Research Ethics Committee (reference 196 11/NW/0382) and the present study was conducted based on application 46 007. 197 Currently, Magnetic Resonance Imaging (MRI) data and Imaging-Derived Phenotypes (IDPs) 198 are available for about 41 000 participants. This study analyzed the IDPs from the first imaging 199 visit generated by an image-processing pipeline developed and run by the UK Biobank Imaging 200 team (Alfaro-Almagro et al., 2018; Miller et al., 2016). 201 2.1.1. Brain Image Acquisition and Processing. 202 A standard Siemens Skyra 3T running VD13A SP4 with a standard Siemens 32-channel RF 203 receive head coil was used to collect data (Brain Scan Protocol). The 3D MPRAGE T1-weighted 204 volumes were analyzed by the UK Biobank Imaging team with pipeline scripts that primarily call 205 for FSL and Freesurfer tools. Details of the acquisition protocols, image processing pipeline, image 206 data files and derived measures IDPs of brain structure and function are available in the UK 207 Biobank Imaging Protocols. 208 2.1.2. Total Brain Volume (TBV) 209 TBV was calculated as the sum of the total grey matter volume (GMV; i.e., sum of cortical 210 and subcortical GMV, data-field 26518), cerebellum white matter volume (WMV, data-fields 211 26556 for left and 26587 for right), and cerebral WMV (data-fields 26553 for left and 26584 for 212 right) from the UK Biobank ASEG Freesurfer segmentations. Refer to Supplemental Info 1 for 213 more on the choice of TBV. Individuals with missing data for these regions were excluded from 214 the analyses, yielding 40 055 participants. 215 2.1.3. Scanner Site 216 The age and sex of participants differed across the 3 scanner sites located in Cheadle 217 (Site 11025), Reading (Site 11026), and Newcastle (Site 11027; See Supplemental Info 1). One 218 individual without scanner site was removed from the analyses yielding 40 054 participants. Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 9 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

219 2.1.4. Sex 220 Participants who did not self-report as male or female or whose self-reported sex and genetic 221 sex differed were also excluded from the analyses (N = 26). When genetic sex was not available, 222 reported-sex was used to define the sex of the participant. Of the 40 029 participants included in 223 the analyses, there were more females (N= 21 142) than males (N = 18 886, χ2(1) = 127.15, p < 224 2.2e-16). 225 2.1.5. Age 226 To obtain a continuous and more precise measure of age, age was calculated based on the year 227 and month of birth of the participant and the day, month, and year of their MRI visit. Mean age 228 was at 63.70 years old (SD = 7.54). Males (M = 64.39 years, SD = 7.65) were older than females

229 (t (39180) = -17.18, p < 2.2e-16, M = 63.09 years, SD =7.39). 230 2.2. Image Derived-Phenotypes (IDPs) 231 The descriptive statistics of all global and regional IDPs analyzed in the present study and their 232 respective data-fields and segmentation origin are listed in Supplemental Table A1. The majority 233 of IDPs correspond to grey matter, since white matter volumes were not segmented by the UK 234 Biobank Imaging team. 235 2.2.1. Global IDPs 236 A total of 9 global IDPs were investigated: TBV, Total Mean Cortical Thickness (Total MCT), 237 Total Surface Area (TSA), Subcortical GMV, Cortical GMV, Cerebral WMV, Cerebellar GMV, 238 Cerebellar WMV, and the Brainstem volume. 239 WMV measures were obtained by summing left and right global measures from Freesurfer 240 ASEG segmentations (data-field 190). Cerebellum GMV was calculated as the sum of the 241 cerebellar volumes from the FAST segmentations (data-field 1101). Total MCT and TSA were 242 respectively calculated as the sum of the mean cortical thickness and surface area measures from 243 the Freesurfer a2009s segmentations (data-field 197). The whole brain stem measure was taken 244 from the Freesurfer subsegmentations (data-field 191) and the Subcortical GMV measure was 245 calculated as the sum of the left and right whole amygdala, hippocampus, and thalamus volumes 246 from the Freesurfer subsegmentations (data-field 191) and the left and right caudate, accumbens, 247 pallidum, and putamen of the Freesurfer ASEG segmentations (data-field 190). 248 Based on the recommendations from the UK Biobank Imaging Protocols, we excluded 249 Freesurfer IDPs when T2-FLAIR was not used in addition to the T1 images to obtain the Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 10 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

250 segmentations from Freesurfer a2009s (volume, surface area, and mean thickness) and Freesurfer 251 subsegmentations. Moreover, 790 individuals had missing values for all FAST cerebellum 252 segmentations and were excluded from the FAST segmentation analyses. 253 Thus, while 40 028 individuals were included in the analyses for TBV, Cerebellum WM, and 254 Cerebral WM, 39 238 individuals were included in the analyses with FAST segmentations and 38 255 710 were included in the analyses of the Freesurfer Subsegmentations and Freesurfer a2009s 256 segmentations. Missing values and null segmentations (e.g., 0 mm3) for a region were replaced by 257 the mean of that region when calculating global measures. See Supplemental Info 3 for correlations 258 between the global measures provided by Freesurfer ASEG and those calculated from the FAST, 259 Freesurfer Subsegmentations, Freesurfer ASEG, and Freesurfer a2009s Segmentations. 260 2.2.2. Regional IDPs 261 A case-wise participant exclusion strategy was applied to each IDP for the regional 262 analyses: participants with a missing value or a segmentation error for a region were excluded 263 from the analyses of that region but were maintained in the analyses of other IDP. Following visual 264 examination of the distribution of regional cerebral measures, values 3 times the inter-quartile 265 range for a region were considered to be segmentation errors and were removed from the analyses 266 of that region. 267 A total of 620 regional IDPs were investigated: 444 cortical regions (148 volumes, 148 268 surface areas, and 148 cortical thicknesses) from the Freesurfer a2009s segmentations (Destrieux 269 Atlas, data-field 197), 116 whole segmentations and subsegmentations of the amygdala, 270 hippocampus, and thalamus and subsegmentations of the brainstem (Freesurfer subsegmentations, 271 data-field 191), 28 cerebellum GMV segmentations from the FAST segmentations (data-field 272 1101), and 32 subcortical, white matter, and ventricle volumes from the Freesurfer ASEG 273 segmentations (data-field 190). Freesurfer subcortical segmentations for the caudate, putamen, 274 accumbens, and pallidum were used instead of the preregistered FIRST volumes, for segmentation 275 consistency with the other subcortical and cortical volume which were segmented from 276 Freesurfer. 277 2.3. Statistical Analyses 278 Analyses were preregistered on OSF and run using R (R Core Team, 2019). The preregistration 279 and code are on OSF (https://osf.io/s4qc5/?view_only=bb067d96d0df4ae4902f99747d60e828). 280 Used packages are listed in Supplemental Info 7. Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 11 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

281 282 2.3.1 Data Transformation. 283 To examine allometric scaling, regional and global measures were log10 transformed. All 284 continuous variables were centered around the mean in order to examine the effects of a variable 285 when other variables are at their mean value. The categorical sex variable was coded -0.5 for males 286 and 05 for females. The scanner site variable was dummy coded with the largest site, Cheadle (Site 287 1102), as reference. 288 2.3.2. Analyses. 289 Global and Regional analyses were performed twice. Once without scaling (dividing by 1 290 SD) to obtain the allometric scaling coefficient for each brain region and once with scaling to 291 report standardized betas as effect sizes. Non-linear effects of age were modeled with quadratic 292 age over spline regression as spline regressions do not yield interpretable beta coefficients of age. 293 Isometry was tested using the linear hypothesis function which tests if scaling coefficients obtained 294 without scaling variables differ from 1. Scanner site (Cheadle - Site 1102, Reading - Site 11026, 295 and Newcastle - Site 11027) was additionally added as a covariate, although it was omitted from 296 the preregistration. 297 2.3.3. Global Analyses. 298 Global analyses were conducted to evaluate how TBV varies with age, age2, and sex 299 (equation 1) and how TSA, Total MCT, Cerebral GMV, Cerebral WMV, Total Subcortical GMV, 300 Cerebellum GMV, Cerebellum WMV, and the brainstem volume vary with TBV, age, age2, and 301 sex (equation 2). 302 303 Equation 1 304 Log10(TBV)= Intercept + β1*Age+ β2*Sex+ β3*Age2+ β4*Age x Sex+ β5*Age2 x Sex+β6* 305 Scanner Site+ Error 306 Equation 2 307 Log10(Global Measure) = Intercept + β1*Log10(TBV)+ β2*Age+ β3*Sex+ β4*Age2+ 308 β5*Log10(TBV) x Sex + β6*Log10(TBV) x Age+ β7 *Log10(TBV) x Age2+ β8*Age x Sex+ 309 β9*Age2 x Sex+ β10*Log10(TBV) x Age x Sex + β1*Log10(TBV) x Age2x Sex +β12*Scanner Site 310 + Error 311 Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 12 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

312 2.3.4 Regional Analyses. 313 Regional analyses were conducted to evaluate how regional volumes, surface areas, and 314 cortical thicknesses vary with TCM, age, age2, and sex with equation 3. The TCMs were TBV for 315 volumes, total MCT for mean thicknesses, and TSA for surface areas. 316 317 Equation 3 318 Log10(Region) = Intercept + β1*Log10(TCM)+ β2*Age+ β3*Sex+ β4*Age2+ β5*Log10(TCM) x 319 Sex + β6*Log10(TCM) x Age+ β7 *Log10(TCM) x Age2+ β8*Age x Sex+ β9*Age2 x Sex+ 320 β10*Log10(TCM) x Age x Sex + β1*Log10(TCM) x Age2x Sex +β12*Scanner Site + Error 321 322 2.3.5 Person-level Neuroanatomical Markers. 323 To obtain a global and regional marker of an individual’s deviance from the norm in terms 324 of volume, mean thickness, and surface area, we extracted the residuals from each dependent 325 variable. The residuals were obtained from the model where continuous variables were centered 326 but not scaled to maintain differences in magnitude across regions. An individual’s residual value 327 for a given regional measure reflects that individual’s deviance from the norm, given his/her age, 328 sex, and TCM, and therefore constitutes a new neuroanatomical marker. 329 330 2.3.6 Person-level Global Neuroanatomical Deviance. 331 From the person-level local neuroanatomical markers, we generated four person-level 332 global neuroanatomical deviance measures with equation 4: one for volumes, one for mean 333 thicknesses, one for surface areas, and one for all regions. The person-level global neuroanatomical 334 deviance measure corresponds to a person’s global neuroanatomical deviance from the norm. 335 Although we pre-registered equation 4 without dividing by the total number of investigated regions 336 for a global measure (N), we did so to obtain a value reflecting mean deviation relative to the norm. 337 Considering that all IDPs were not available for all individuals, we excluded participants with 338 more than 10% of missing data across regional IDPs. The cerebral marker across brain measures, 339 which was not preregistered, was calculated by averaging the Z-score of the volumetric, cortical 340 mean thickness, and cortical surface area global neuroanatomical deviance marker. 341 342 Equation 4 Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 13 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

343 Global Neuroanatomical Deviance= (∑ (Person-Level Neuroanatomical Markers)2) / N 344 345 2.3.7 Exploratory Analyses. 346 These analyses were not preregistered unless otherwise stated (for more details see 347 Supplemental Info 4). In brief, we first examined whether global and regional measures were 348 allometric with the linearHypothesis function from the car R package (Fox et al., 2020) with the 349 null hypothesis being “The slope of log10(TCM) is equal to 1”. Then, we examined whether the 350 scaling coefficient of mean thicknesses with TBV differed from ⅓ and whether the scaling 351 coefficient of surface areas with TBV differed from ⅔ with the linearHypothesis function (Fox et 352 al., 2020) and appropriate null (e.g., null hypothesis for mean thicknesses: “The slope of 353 log10(TBV) is equal to 1/3”). We would expect these coefficients if brain growth was proportional 354 (similar to a sphere) and if larger brains were scaled-up versions of smaller brains. Third, we 355 examined sex differences in variance with a Levene’s test (F-test) and calculated as the variance 356 ratio as Female SD / Male SD. Fourth, we compared the results of our main analysis to those 357 obtained when using a linear covariate TCM adjustment (i.e., equation 4 without the log 358 transformation) and when using the proportion adjustment for TCM (i.e., dividing a region by 359 TCM to obtain an adjusted region measure and running equation 4 on the adjusted region without 360 the log transformation and the main effect of TBV). Fifth, as preregistered, we attempted to 361 replicate previous studies on cerebral sex differences that considered brain allometry. Sixth, we 362 replicated Ritchie and colleagues’ (2018) analyses of the Desikan-Killiany cortical measures and 363 FIRST subcortical volumes with the linear covariate TCM adjustment. We additionally ran the 364 same analyses with the allometric TCM adjustment to examine whether we observed the same 365 effects of omitting brain allometry when investigating sex differences in the UK Biobank using 366 different cerebral segmentations and statistical analyses. 367 2.3.8 Multiple Comparison Corrections. 368 Considering that 620 regions and 11 beta coefficients were investigated for regional IDPs, 369 three thresholds of significance were used: 0.05/11, 0.05/620, and 0.05/ (11 * 620). The same 370 rationale was applied to the global IDPs, with the following thresholds for TBV 0.05/5, 0.05/9, 371 and 0.05/ (5 * 9) and for the remaining global measures: 0.05/11, 0.05/9, and 0.05/ (11 * 9). 372 Significant variance ratio differences are reported at p < 0.05/629 (sum of global and regional 373 cerebral measures). Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 14 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

374

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 15 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

375 3. Results and Discussion

376 To avoid redundancy, results are sequentially discussed. Only results at the strictest level 377 of significance are reported in text: p < 0.05/ (5*9) for TBV, 0.05/ (11*9) for other global 378 measures, p < 0.05/ (11*620) for regional measures, and p < 0.05/629 for sex differences in 379 variance. Scaling coefficients (α) correspond to the estimate when continuous variables are 380 centered, and standardized betas (β) reflect the estimate when continuous variables are centered 381 and scaled (1 SD). 382 Descriptive statistics are available in Supplemental Tables A2-14. Regression results by 383 region are available in Supplemental Tables B1-B10 and by main effectsor interaction, in 384 Supplemental Tables C1-C15. See Supplemental Tables D2-D5 for statistics on regional 385 deviance from isometry. Correlations between the left and right region in terms of the scaling 386 coefficient with the TCM, the age standardized betas, and sex standardized betas are available on 387 OSF, in Supplemental Figures File 388 1(https://osf.io/s4qc5/?view_only=bb067d96d0df4ae4902f99747d60e828) and correlations 389 between cortical scaling, sex, and age coefficients are available in Supplemental Table C1. 390 391 3.1 Allometry 392 3.1.1 Global Allometry 393 All global scaling coefficients were hypoallometric (α ranging from 0.03 to 0.91), 394 suggesting that these regions increase less than TBV as TBV increases, except for cerebral WMV, 395 which was hyperallometric (α = 1.21). The scaling coefficient of TSA with TBV significantly 396 differed from the theoretical value 2/3 (α = 0.89) and the scaling coefficient of Total MCT with 397 TBV differed from 1/3 (α = 0.03). In cerebellar GMV, all regions were hypoallometric (α = 0.50 - 398 0.95), except for 4 isometric regions (α = 0.93 - 0.95). Ventricles and the cerebral spinal fluid were 399 hypoallometric (α = 0.40 - 1.01), except for the lateral ventricles (left α = 1.01 and right α = 0.96). 400 The optic chiasm, corpus callosum, cerebellum WMV, and ventral diencephalon measures were 401 hypoallometric (α = 0.55 - 0.93), whereas for the mid-anterior segmentation of the corpus callosum 402 which was isometric (α = 0.99). 403 Allometric coefficients were generally consistent with previous studies that report 404 hyperallometry in cerebral WMV (Jong et al., 2017; Toro et al., 2009) and hypoallometry in the 405 majority of cerebellar (Mankiw et al., 2017), subcortical (Jong et al., 2017; Liu et al., 2014; Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 16 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

406 Reardon et al., 2016; Williams et al., 2020), and corpus callosum volumes (Lefebvre et al., 2015). 407 See Supplemental Table D1 for global deviance from allometry. 408 3.1.2 Cortical Allometry 409 TBV was a significant positive predictor of all volumes, TSA of all surface areas, and Total 410 MCT of all mean thicknesses. Scaling coefficients varied across regions and measures (Table 1). 411 The scaling coefficients of cortical volumes were highly correlated to those of cortical surface 412 areas (r = 0.85, p < 2.2e-16) but were not correlated to those of cortical mean thicknesses (r = - 413 0.05, p = 0.535). In cortical regions, 98 volumes, 62 areas, and 63 mean thicknesses were 414 hypoallometric (α = 0.60 - 0.96), while 18 volumes, 50 areas, and 58 mean thicknesses were 415 hyperallometric (α = 1.04-1.62), and 32 volumes, 36 areas, and 27 mean thicknesses were 416 isometric (α = 0.94-1.11; Figure 1). 417 These findings mirror those reported by Liu and colleagues (2014) and Reardon and 418 colleagues (2018), who found that scaling across cortical regions is heterogeneous, covering a 419 wide range of hypoallometry, isometry, and hyperallometry values. Similarly to Reardon and 420 colleagues (2018), who studied the scaling relationship between vertex area and cortical surface 421 area, surface areas were hyperallometric in the middle frontal and supramarginal gyri and sulci, 422 and hypoallometric in the sensorimotor cortices (precentral, paracentral, and postcentral gyri and 423 sulci), occipital temporal regions, and some cingulate (anterior, mid-anterior, and post dorsal) and 424 callosal (sub and pericallosal) regions. 425

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 17 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

426

427 428 Figure 1. Scaling Coefficients of Cortical Surface Areas, Mean Thicknesses, and Volumes with 429 Total Brain Volume (TBV). Values are the scaling coefficients of a region with TBV and range 430 from 0.61 (volume of the right posterior ramus of lateral sulcus) to 1.63 (mean thickness of the 431 left paracentral gyrus and sulcus). The flat representation corresponds to the flattened image of 432 the superior view with the midline of the circle reflecting regions within the sagittal plane and 433 circle edges reflecting inferior regions. Figures made with https://neuroanatomy.github.io/cortex/ 434 (Toro, 2020).

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 18 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

435 436 3.1.3 Subcortical Allometry 437 All subcortical volumes were hypoallometric (α = 0.49 - 0.92) except for the right lateral 438 posterior and the right limitans suprageniculate nuclei, which were isometric (α = 0.95, α = 1.08, 439 respectively), and the left limitans suprageniculate nuclei and left accumbens area, which were 440 hyperallometric (α = 1.17, α = 1.11, respectively). 441 General hypoallometry across whole subcortical structures is consistent with previous 442 findings (Jäncke et al., 2015b; Liu et al., 2014; Williams et al., 2020). As for allometry within 443 subcortical structures, Reardon and colleagues (2018) are the only ones to date that examined and 444 reported variations in scaling within subcortical structures. However, the latter study examined the 445 scaling relationship of the vertex area of subcortical subregions with cortical area, whereas the 446 present study examined volumetric variations within these regions. Thus, our finding that 447 allometry varies within subcortical volumes extends our understanding of the cerebral scaling 448 relationships between regional and global measures. 449 450 3.1.4 Mean Thickness and Surface Area Scaling with TBV 451 Exploratory analyses on the scaling relationship between TBV and cortical mean 452 thicknesses or surface areas revealed that the scaling coefficients of all mean thicknesses with TBV 453 were different from one-third, whereas the scaling coefficients of 19 regional surface areas with 454 TBV did not differ from two-thirds (Supplemental Tables D6-7). 455 This study adds the literature suggesting that larger brains are not simply a scaled-up 456 version of smaller brains (Finlay et al., 2001; Im et al., 2008; Toro et al., 2008), as the first study 457 to examine scaling coefficients of regional cortical surface areas and mean thicknesses with TBV 458 that go beyond lobar segmentations. If the brain regions grew proportionally to brain size, total 459 MCT would scale to the power of one-third with TBV, and TSA to the power of two-thirds with 460 TBV (Finlay et al., 2001). Yet, we find that total MCT scaled to the power of 0.03 with TBV and 461 that the majority of cortical mean thicknesses had allometric scaling coefficients close to 0, 462 reflecting the stability of cortical mean thicknesses with TBV growth. Moreover, TSA scaled to 463 the power of 0.89 with TBV and the majority of cortical surface areas had hypoallometric scaling 464 coefficients that were greater than two-thirds. The greater than geometrically expected 465 hypoallometry across surfaces can be explained by the dramatic increase in gyrification (Fish et Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 19 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

466 al., 2017), and more specifically, in sulcal convolution, that occurs with the expansion of TBV (Im 467 et al., 2008; Toro et al., 2008). Finally, the heterogeneity of allometric patterns observed across 468 the cortex may be explained by the nonuniform gyrification of the cortical surface (Fish et al., 469 2017). 470 471 3.1.5 Sex or Age-Dependent Allometry 472 Allometry depended on sex (0.2%, 12/628) or age (11%, 71/628) in relatively few regions 473 (details in Supplemental Info 5.1). Sex differences in allometry were less frequent, although larger 474 (|α| = 0.05 - 0.12), than age differences in allometry (|α| = 0.01 - 0.04). Regional volumes generally 475 increased less with TBV in females, while mean thicknesses increased less with Total MCT in 476 males. Although sparse, the presence of TCM interactions with age or sex suggest that matching 477 individuals between groups by TCM may not be appropriate for all regions, as cerebral sex 478 differences may reflect sex-dependent distributions of tissues instead of individual differences in 479 brain size (Luders et al., 2009). Considering that these interactions are often overlooked in studies 480 examining sex and age differences (e.g., Ritchie et al., 2018; Vinke et al., 2018), we suggest that 481 they be considered to obtain unbiased estimates of age and sex effects on the brain and to 482 accurately identify associations between brain regions and behavioral or cognitive traits. 483 484 3.1.6 Conclusion on Allometry 485 All brain regions varied with global brain measures, and the majority (86%) were 486 allometric as they scaled non-linearly with their TCM. Of the regions exhibiting allometry, 487 hypoallometry was reported in 93% of volumes, 55% of the cortical surface areas, and 52% of the 488 cortical mean thicknesses (Table 1). While the association between scaling and cognition and 489 behavior remains unknown, our study adds to the literature (Finlay et al., 2001; Jäncke et al., 490 2015b, 2019; Jong et al., 2017; Toro et al., 2009) supporting allometric scaling as an inherent 491 property of the brain that varies across regions and cerebral measures, and provides scaling 492 coefficients for regions that were not previously investigated (e.g., subcortical subsegmentations, 493 ventricles etc.). 494

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 20 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

495 496 Table 1. Cerebral Regions Exhibiting Brain Allometry. 1st Media Me 3rd Measure N % Min. Max Qu. n an Qu. Cortical Surface Hypoallometric 62 42 0.64 0.76 0.83 0.82 0.91 0.95 Areas (N = 148) Hyperallometric 50 34 1.06 1.1 1.13 1.16 1.21 1.39

Cortical Mean Hypoallometric 63 43 0.66 0.78 0.84 0.83 0.89 0.96 Thicknesses (N = 148) Hyperallometric 58 39 1.04 1.09 1.14 1.2 1.31 1.62

Cortical Volumes Hypoallometric 98 66 0.6 0.73 0.82 0.8 0.89 0.96 (N = 148) Hyperallometric 18 12 1.05 1.07 1.1 1.15 1.16 1.59 Freesurfer Hypoallometric 113 97 0.49 0.68 0.75 0.74 0.8 0.92 Subcortical Subsegmentation Hyperallometric 1 1 1.17 1.17 1.17 1.17 1.17 1.17 Volumes (N = 116) FAST Cerebellar Volumes Hypoallometric 24 86 0.5 0.68 0.74 0.75 0.82 0.94 (N = 28) ASEG Subcortical Hypoallometric 7 88 0.69 0.73 0.75 0.78 0.81 0.92 Volumes (N = 8) Hyperallometric 1 13 1.11 1.11 1.11 1.11 1.11 1.11

ASEG Ventricle & CSF Volumes Hypoallometric 7 70 0.4 0.47 0.49 0.51 0.55 0.62 (N = 10)

ASEG Cerebellum, Hypoallometric 12 86 0.55 0.66 0.78 0.76 0.85 0.93 Corpus Callosum, Ventral DC, Optic Chiasm Volumes Hyperallometric 1 7 1.21 1.21 1.21 1.21 1.21 1.21 (N = 14) Global Measures Hypoallometric 8 89 0.03 0.77 0.73 0.83 0.9 0.91 (N = 9) Hyperallometric 1 11 1.21 1.21 1.21 1.21 1.21 1.21 N.B. Values displayed are allometric scaling coefficients (α). Hyperallometric α > 1, and Hypoallometric: α <1. CSF: Cerebral Spinal Fluid. DC: Diencephalon. 497 498

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 21 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

499 3.2 Sex Differences 500 3.2.1 Global Measures 501 TBV was significantly larger in males than in females (β = - 1.14). Once TBV was adjusted 502 for with the allometric adjustment (equation 3), the cerebellar WMV (β = 0.27), cerebellar GMV 503 (β = 0.25), total MCT (β = 0.12), and cerebral WMV (β = 0.06) were greater in females, while 504 brainstem volume (β = -0.21), total subcortical volumes (β = -0.08), TSA (β = -0.07), and cerebral 505 GMV (β = -0.02) were greater in males. 506 Consistent with previous studies, males had a larger TBV (e.g., Ritchie et al., 2018; 507 Ruigrok et al., 2014), while females had a relatively larger Total MCT (Im et al., 2008, p. 200; van 508 Velsen et al., 2013). However, we did not find that males and females had a similar TSA (Im et 509 al., 2008), nor did we observe greater cerebral WMV in males relative to brain size (Chen et al., 510 2007; Gur et al., 1999). Instead, our analyses revealed that males have a larger TSA and females a 511 greater cerebral WMV. Considering the small magnitude of these sex differences (<0.1) and the 512 sample size of the previous studies (N < 150), we speculate that these studies were not sufficiently 513 powered to reliably estimate these effects. 514 3.2.1 Cerebellar GMV 515 The Freesurfer ASEG Cerebellum GMV – used to calculate TBV - was larger in males (β 516 = - 0.36), whereas the FAST Cerebellum GMV - calculated as the sum of the cerebellar lobes and 517 vermes from FAST Diedrichsen Cerebellar Atlas - was larger in females (β = 0.25). 518 Result discrepancies between segmentation algorithms may stem from Diedrichsen’s 519 segmentation algorithm ignoring individual WMV and GMV intensities, which are taken into 520 account by Freesurfer. Or differences may be due to Freesurfer over-labelling peripheral tissue as 521 it is more sensitive in regions of low contrast between tissue types (Carass et al., 2018). Although 522 the cerebellar GMV of the FAST and ASEG segmentations only correlated at 76%, discrepancies 523 across cerebellar segmentations did not influence our measure of TBV, as the TBV calculated by 524 summing regional segmentations (including the FAST GMV) correlated at 99.8% with our 525 measure of TBV (derived from the ASEG segmentations). 526 3.2.3 Regional Cerebellar GMVs 527 When examining sex differences in the cerebellum with the FAST cerebellum regional 528 segmentations, females had larger cerebellar GMV in 82% of regions (23/28) with coefficients 529 ranging from 0.08 (Right Crus I) to 0.64 (Vermis X). The crus I vermis and the left and right lobule

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 22 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

530 V did not differ between sexes and the left and right lobule X were larger in males (β = -0.17, β = 531 -0.12, respectively). 532 Our findings contrast with the literature on sex differences within cerebellum (review in 533 Han et al., 2020). For instance, Han and colleagues (2020) instead reported that the VIIIA lobules 534 were larger in males and that the right I–III lobules, and IX and X Vermes were larger in females 535 when adjusting for intracranial volume with the linear covariate method. Moreover, in our 536 replication of Mankiw and colleagues’ (2017) study, we found that, instead of being greater in 537 males, the cerebellum, flocculus, cerebellar lobule VIIb, VIIb, and VIIA, and Crus II volumes were 538 greater in females and that the flocculus volume did not vary between sexes. Although both studies 539 used segmentation algorithms that have a better parcellation accuracy than the SUIT segmentation 540 (Diedrichsen et al., 2009) of the present study (Carass et al., 2018; S. Han, Carass, et al., 2020), 541 discrepancies in the literature may also stem from differences in sample age (mean age = 12.5 and 542 70 years old, respectively) and size (N = 116 and 2,023, respectively). 543 In light of the difficulty of segmenting the cerebellum and the differences in regional 544 specificity and accuracy across segmentations, we suggest that future studies take advantage of the 545 large UK Biobank dataset to apply and compare cerebellar segmentation algorithms. 546 547 3.2.4 Whole Subcortical Volumes 548 The thalamus (Right β = -0.15, Left β = -0.08), putamen (Left and Right β = -0.18), left 549 pallidum (β = -0.08), and left amygdala (β = -0.12) were larger in males and the hippocampus 550 (Right β = 0.07, Left β = 0.06) and left accumbens were larger in females (β = 0.10). The right 551 pallidum volume, the caudate volumes, and the right accumbens area volume did not differ 552 between sexes. 553 Our findings are consistent with previous studies reporting greater thalamic volume in 554 males (Lotze et al., 2019) and larger hippocampal volumes in females (Malykhin et al., 2017; 555 Nordenskjöld et al., 2015), although they contrast with research supporting the absence of sex 556 differences in the amygdala (Lotze et al., 2019) and the hippocampus (Ritchie et al., 2018; Tan et 557 al., 2016) or greater male hippocampal volume (Lotze et al., 2019; Pintzka et al., 2015). And yet, 558 we similarly find that males have larger putamen, pallidum, and left amygdala volumes in our 559 replication of studies examining sex differences when considering brain allometry (Reardon et al., 560 2016; Sanchis-Segura et al., 2019). Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 23 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

561 We additionally replicated Ritchie and colleagues’ (2018) findings that males had greater 562 pallidum, putamen, and amygdala volumes, when adjusting for TBV with the linear covariate 563 adjustment and analyzing FIRST subcortical segmentations. For a detailed analysis of the 564 replication by region see Supplemental Info 6.4.2 and Supplemental Tables G5-9. 565 When adjusting for TBV with the linear covariate or the allometric approach in the 566 replication models with the FIRST segmentations, we found similar subcortical sex differences to 567 those reported in our main analyses with the Freesurfer segmentations with some exceptions. 568 Specifically, instead of being larger in males, the left thalamus was larger in females and right 569 thalamus did not show sex differences in the replication models. Moreover, the right accumbens 570 area was larger in females and the right pallidum was larger in males in the replication analyses, 571 although they did not differ between sexes in the main analyses. These discrepancies may stem 572 from the different terms and interactions included in the main and replication analyses or from 573 differences between the FIRST and Freesurfer subcortical segmentations. For instance, FIRST 574 provides a segmentation of the amygdala more similar to that of manual tracing than Freesurfer 575 (Morey et al., 2009), although the amygdala agreement with manual segmentation is relatively 576 poor compared to other regions such as the hippocampus (Morey et al., 2010), potentially due to 577 the complexity of the structure (Schoemaker et al., 2016). 578 Sex differences from our main analyses additionally varied across hemispheres. For 579 instance, the amygdala volume was larger for males in the left hemisphere and similar across sexes 580 in the right hemisphere. However, seemingly inconsistent results on whole subcortical structures 581 may be illuminated by examining their subcomponents, as provided by the Freesurfer subcortical 582 subsegmentations. 583 3.2.5 Subcortical Subsegmentations 584 Sex differences were found in 67% of the subcortical subsegmentations (74/110), with 585 greater male volume in 42 (38%) regions and greater female volume in 32 (29%) regions (details 586 in Supplemental Info 5.2.3). 587 The magnitude of the subsegmentation subcortical sex differences was not perceptible at 588 the whole subcortical level due to the presence of sex differences in opposite directions. For 589 instance, medial and lateral regions of the thalamus were considerably larger in females (β ranging 590 from 0.06 to 0.25), although the whole thalamus volume was greater in males (Right β = -0.15, 591 Left β = -0.08). Moreover, the right cortical nucleus (β = 0.13) was larger in females even though Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 24 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

592 sex differences were absent in the whole right segmentation of amygdala. Taken together, these 593 findings support a high variability of sex differences within subcortical structures and highlights 594 the importance of favoring fine-grained segmentations, as done in this study, to better understand 595 where cerebral sex differences lie. 596 3.2.6 Cortical Regions 597 Cortical sex differences were present in 57% of surface areas (84/148) and 66% of volumes 598 (97/148) and mean thicknesses (98/148). No clear spatial trend in sex differences was apparent 599 across lobes. In terms of cortical volumes, 62 regions (42%) were larger in males, ranging from - 600 0.27 (right occipital pole) to -0.06 (right inferior temporal sulcus), and 35 regions (24%) were 601 larger in females, ranging from 0.06 (right precentral gyrus) to 0.26 (right postcentral gyrus). As 602 for cortical mean thicknesses, 50 regions (34%) were greater in males and 48 (32%) were greater 603 in females. Greater mean thicknesses in males varied from -0.39 (left medial orbital – olfactory- 604 sulcus) to -0.05 (parieto-occipital sulcus or fissure), while greater mean thicknesses in females 605 ranged from 0.06 (left transverse frontopolar gyri and sulci) to 0.31 (left transverse temporal 606 sulcus). Finally, in terms of cortical surface areas, males had larger surface areas in 50 regions 607 (34%) ranging from -0.22 (right medial occipito-temporal-collateral – sulcus and lingual sulcus) 608 to -0.06 (left precentral gyrus), and females had larger surface areas in 34 regions (23%) with 609 coefficients ranging from 0.06 (left superior frontal sulcus) to 0.21 (right anterior transverse 610 temporal gyrus of Heschl; Figure 3). 611 We replicated the majority of sex differences (88%, 90/98) reported by Ritchie and 612 colleagues (2018) with the Desikan-Killiany Cortical segmentations when adjusting for TCM with 613 the linear covariate approach. We observed significant sex differences in additional regions (81%, 614 150/186), possibly due to our larger sample size. Sex differences from the main analyses with the 615 Destrieux segmentation and the replication analyses with the Desikan-Killiany appeared to be 616 generally consistent. 617 In line with a study of cortical volumetric sex differences in 411 middle aged participants 618 (Chen et al., 2007), we found that males had a larger left inferior temporal gyrus and larger right 619 occipital lingual and right middle temporal gyri, while females had a larger right inferior parietal 620 gyrus, right post-dorsal part of the cingulate gyrus and sulcus, and left and right mid-anterior and 621 post-ventral parts of the cingulate gyrus. Consistent with a study of 2 838 middle aged adults 622 (Lotze et al., 2019), we found that females have larger volumes in the superior parietal lobe and Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 25 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

623 right orbitofrontal cortex, whereas males have larger volumes in the left temporal pole and right 624 fusiform gyrus. Yet, in contrast with the previous literature on sex differences in GMV (Lotze et 625 al., 2019; Ritchie et al., 2018; Ruigrok et al., 2014), we reported that females have a larger 626 precentral gyri than males and that males have a larger right anterior part of the cingulate gyrus 627 and sulcus than females. Moreover, we did not find sex differences in the left anterior part of the 628 cingulate gyrus and sulcus, although past studies suggest that this volume was larger in females 629 (Lotze et al., 2019; Ruigrok et al., 2014). The divergence in some of the presented results can 630 partly be attributed to differences in sample size, varying neuroimaging techniques, and to the 631 small size of these effects (median |β| = 0.09) as well as to differences in sample age range. And 632 yet, we observed a similar pattern of sex differences in our replication of Ritchie and colleagues’ 633 (2018) analyses with the allometric adjustment for TCM, suggesting that the different terms 634 included in our models and the differences between the Destrieux and the Desikan-Killiany Atlases 635 had little influence on the majority reported cortical sex differences. 636

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 26 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

637

638 639 Figure 2. Sex Differences across Cortical Measures. Sex effects differences from -0.40 (mean 640 thickness of the left medial orbital sulcus) to 0.32 (mean thickness of the left transverse temporal 641 sulcus). Negative effects reflect greater male than female volumes. The flat representation 642 corresponds to the flattened image of the superior view with the midline of the circle reflecting 643 regions within the sagittal plane and circle edges reflecting inferior regions. Figures made with 644 https://neuroanatomy.github.io/cortex/ (Toro, 2020).

645

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 27 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

646 3.2.7 Sex Differences in Variance 647 In addition to observing mean sex differences in two-thirds of regions, we found sex 648 differences in variance in 49% (306/629) of regions. A total of 253 (40%) regions exhibited greater 649 male variability and 56 (9%) exhibited greater female variability (Table 2). Sex differences in 650 variance ranged from 0.82 (for the right cerebellar lobule VIIIa, implying greater male variability) 651 to 1.17 (for the optic chiasm; Supplemental Info 6.1 and Supplemental Tables E1-7). 652 As reported by previous studies (Ritchie et al., 2018; Wierenga et al., n.d., 2018, 2019), 653 the majority of brain regions with sex differences in variance were more variable in males (82%) 654 compared to females (18%). Mean thicknesses were generally more variable in females, while 655 volumes and surface areas were more variable in males. Overall, cerebellar lobes and vermes were 656 also more variable in males. Sex differences in variance across subcortical subsegmentations were 657 greater in males in the hippocampus, amygdala, and thalamus. In terms of whole subcortical 658 volumes, both the hippocampus, which was larger in females, and caudate, which did not show 659 mean sex differences, were more variable in males. Finally, regions that were larger in one sex 660 were typically more variable in the other sex. 661 Differences in variance thus do not appear to be a mechanical consequence of differences 662 in mean, and instead may reflect a distinct phenomenon known as the greater male variability 663 hypothesis. This hypothesis states that males are more variable than females across a variety of 664 psychological and physical characteristics (Ellis, 1894) and is widely supported by a range of 665 human (e.g., Johnson et al., 2008; Ju et al., 2015; Karwowski et al., 2016; Lehre et al., 2009; 666 Wierenga et al., 2019) and animal (e.g., Branch et al., 2020; DeCasien et al., 2020) studies. 667 Although the mechanisms behind the greater male variability hypothesis exceed the scope of the 668 present study, our findings further support greater male variability, which extends well beyond 669 brain measures. 670

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 28 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

671 672 Table 2. Variance Ratios of Sex Differences across Segmentations Segmentation Sex min 1st median mean 3rd max Differences in Qu. Qu. Variance Ratio N %

Cortical Volumes M>F 63 43 0.91 0.94 0.95 0.95 0.96 0.97 (N = 148) M

Cortical Surface Areas M>F 71 48 0.90 0.94 0.95 0.95 0.96 0.97 (N = 148) M

Cortical Mean Thicknesses M>F 26 18 0.9 0.95 0.95 0.95 0.96 0.97 (N = 148) M

Cerebellar Volumes M>F 23 16 0.82 0.90 0.94 0.92 0.95 0.97 (N = 28) M

Subcortical M>F 64 55 0.88 0.93 0.94 0.94 0.96 0.97 Subsegmentations (N = 116)

ASEG Subcortical Volumes M>F 2 25 0.95 0.96 0.96 0.96 0.96 0.96 (N =8)

ASEG Ventricle & CSF M>F 2 20 0.95 0.95 0.95 0.95 0.95 0.96 Volumes (N = 10) M

ASEG Cerebellum, Corpus M>F 5 36 0.93 0.94 0.95 0.95 0.95 0.96 Callosum, Ventral DC, Optic Chiasm Volumes M

Global Measures M>F 1 11 0.90 0.90 0.90 0.90 0.90 0.90 (N = 9) 673 N.B. Values represent Variance Ratios. M: Male, F: Female. Variance Ratio = Female SD / Male 674 SD. Qu.: Quartile. CSF: Cerebral Spinal Fluid.

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 29 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

675 3.2.8 Conclusion on Sex Differences 676 Overall, we found that sex differences in the brain are the rule rather than the exception, 677 affecting two-thirds (419/629) of the investigated brain measures, with 231 regions relatively 678 greater in males. The standardized coefficients (β) of the sex effect of cortical volumes were highly 679 correlated to those of cortical surface areas (r = 0.77, p = 2.28e-43) and moderately so for cortical 680 mean thicknesses (r = 0.45, p = 1.23e-08). 681 Although many of the regional sex differences had very small effect sizes (β < 0.1) and 682 were only significant due to the large sample size, 46% of these cerebral measures (292/629) had 683 a sex difference above 0.1. Specifically, sex differences in cerebellar GMV and WMV, Total MCT, 684 the corpus callosum, and the ventricles were generally greater than 0.1 (details in Supplemental 685 Info 5.2), whereas sex differences in cerebral GMV and WMV, TSA, 51% of subcortical regions 686 and 35 - 45% of the cortical regions were under 0.1. 687 688 3.3 Age Effects 689 3.3.1 Global Measures 690 All cerebral measures decreased linearly with age (β ranging from -0.04 in to -0.33), except 691 for the brainstem volume, TSA, and cerebral WMV which increased (relatively to TBV) with age 692 (β = 0.13, β = 0.11, β = 0.04, respectively). The quadratic age term did not significantly predict 693 cerebral GMV and WMV or the brainstem volume. However, total subcortical volume (β = 0.01) 694 and TSA (β = 0.02) positively, and TBV (β = -0.05), total MCT (β = -0.04), cerebellar GMV (β = 695 -0.05), and cerebellar WMV (β = -0.02) negatively varied with quadratic age. 696 In line with the literature, TBV and Total MCT decreased with linear and quadratic age 697 (Ritchie et al., 2018; van Velsen et al., 2013; Vinke et al., 2018) and Total MCT decreased more 698 rapidly with linear age in males (van Velsen et al., 2013). Yet, our finding that TSA increased with 699 linear and quadratic age contrasts with previous reports of a decrease in surface area across the 700 lifespan (Hogstrom et al., 2013; Lemaitre et al., 2012; Long et al., 2012). Divergent results between 701 our study and those of Hogstrom and colleagues (2013) and Long and colleagues (2012) can be 702 explained by their omission of brain size, as we similarly observed a decrease of TSA with age 703 when excluding TBV from our models. However, when applying the proportion TCM adjustment, 704 as done by Lemaitre and colleagues (2012), we observed an increase in TSA with age, suggesting 705 that differences between our studies may instead stem from differences in segmentation or sample Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 30 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

706 characteristics (e.g., smaller sample (N = 216), wider age range (18 to 87 years old)). Based on 707 our findings, the relative expansion of TSA in older adults with age may reflect a global spread of 708 the sulci, which appears to occur more rapidly in males than females. 709 3.3.2 Cerebellar Volumes 710 There was a linear decline with age of the cerebellar GMV for the FAST (β = -0.20) and 711 the Freesurfer ASEG (β = -0.02) segmentations. However, the FAST cerebellar GMV was also 712 negatively predicted by quadratic age (β = -0.05) and its linear decline with age was quicker in 713 males compared to females (β = 0.03). As for the regional FAST cerebellar GMVs, 27 out of 28 714 (96%) cerebellar volumes decreased linearly with age. The age effect in the cerebellar IX vermis 715 (β = -0.02) did not reach significance. Linear age effects ranged from -0.20 (right Crus I) to -0.05 716 (vermis Crus I). We found a negative quadratic age effect in 74% (20/27) of regions with a linear 717 age effect, which ranged from -0.07 (Left Cerebellar Lobule VIIb) to -0.03 (Right Cerebellar 718 Lobule VIIb). The cerebellar IX vermis was the only area with a quadratic age but no linear age 719 effect (β = -0.04). 720 The linear decrease with age of the cerebellum mirrors previous findings (for review 721 Bernard and Seidler, 2014). The literature also similarly reports a linear rather than a non-linear 722 cerebellar change with age (for review Fjell et al., 2013; Fjell & Walhovd, 2010) and the absence 723 of an age by sex interaction in cerebellar volumes (Hoogendam et al., 2012; Raz et al., 2005) when 724 examining the Freesurfer segmentation of the cerebellum. The discrepancies in results between 725 cerebellar segmentations further highlight the nonnegligible impact that the type of cerebellar 726 segmentation algorithm has on reported results (as discussed in section 3.2.2 and 3.2.3). 727 Although our findings add to the scarce literature on age related changes within the 728 cerebellum, age effects in these GMVs remain highly inconsistent (Bernard & Seidler, 2013; S. 729 Han, An, et al., 2020; Koppelmans et al., 2017). We speculate that these differences in reported 730 results can be attributed to the insufficient sample size of previous studies to investigate the these 731 effects (our median |β|= 0.17; N = 54 for Bernard and Seidler (2013) and N = 213, for Koppelmans 732 et al. 2017) and differences in segmentation algorithms, which vary in accuracy and in the number 733 of segmented cerebellar regions (Carass et al., 2018; L. Han et al., 2019). 734 3.3.3 Whole Subcortical and Subcortical Subsegmentation Volumes 735 The putamen (β = -0.09 for both), accumbens area (Left β = -0.33, Right β = -0.24), 736 amygdala (Left β = -0.16, Right β = -0.14), and hippocampus (Left β = -0.23, Right β = -0.19) Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 31 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

737 decreased with age. The pallidum (Left β = 0.03, Right β = 0.06) and caudate (Left β = 0.12, Right 738 β = 0.15) volumes increased with linear age, whereas the thalamus did not show significant linear 739 age effects. The accumbens area, amygdala, and hippocampus volumes had a negative quadratic 740 age effect, ranging from -0.03 (right accumbens area) to -0.09 (left presubiculum head), and the 741 thalamus, caudate, and right putamen all showed positive quadratic age effects, ranging from 0.02 742 (right putamen) to 0.06 (left caudate). 743 Linear age was a significant predictor of 95% (104/110) of subsegmentations and quadratic 744 age was a significant predictor of 88 (104/110) subsegmentations. Although there were no age 745 effects at the whole subcortical level of the thalamus, we found 24 linear age effects with an 746 absolute effect size greater than 0.1 across thalamic subsegmentations. More positive linear and 747 quadratic age effects were found in ventral and intralaminar thalamic volumes. On the other hand, 748 the majority of the amygdala and the hippocampal subsegmentations (>92%) decreased with age. 749 The direction of the quadratic age effects on subcortical subsegmentations was similar to that of 750 the whole subcortical volumes, as we found negative quadratic age effects across the amygdala 751 and hippocampal subsegmentations and positive quadratic age effects across the thalamic 752 subsegmentations. 753 The volumetric decline in the amygdala, hippocampus, putamen, and nucleus accumbens 754 with age mirrors previous findings (Hogstrom et al., 2013; Kurth et al., 2017; Sele et al., 2020; 755 Vinke et al., 2018). However, our finding of an increase in pallidum volume with age contrasts 756 with past studies reporting a small decrease with age in this region (Sele et al., 2020; Vinke et al., 757 2018). Moreover, while we add to the literature reporting an expansion of the caudate with age 758 (Vinke et al., 2018), a small decrease has also been reported (Sele et al., 2020). In terms of the 759 discrepancy in the caudate results, we speculate that Sele and colleagues’ (2020) sample (N = 231) 760 was insufficient to observe such small changes with age (β = 0.05-0.06). As for the discrepancies 761 in the pallidum results, differences may be attributed to the different terms included in the 762 regressions, as Vinke and colleagues (2018) modeled non-linear changes with splines instead of a 763 quadratic age. 764 3.3.4 Cortical Regions 765 Cortical regions increased with linear age in 22% of volumes, 35% of mean thicknesses, 766 24% of surface areas, and declined with linear age in 41% of volumes, 52% of mean thicknesses, 767 33% of surface areas (Figure 3). Cortical volumes decreased linearly with age in 60 regions, Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 32 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

768 ranging from -0.13 (right precentral gyrus) to -0.02 (right parieto-occipital sulcus), and increased 769 with age in 33 regions, ranging from 0.03 (right superior segment of circular sulcus of the insula) 770 to 0.13 (left central sulcus). Cortical mean thicknesses decreased with age in 77 regions, ranging 771 from -0.14 (right inferior circular sulcus of the insula) to -0.02 (left posterior dorsal cingulate 772 gyrus), and increased with age in 52 regions, ranging from 0.02 (left middle occipital gyrus) to 773 0.22 (right cuneus gyrus). Surface areas increased linearly with age in 36 regions, ranging from 774 0.02 (left superior frontal gyrus) to 0.15 (right central sulci), and decreased with age in 49 regions, 775 ranging from -0.11 (right the orbital sulci) to -0.02 (left lateral aspect of the superior temporal 776 gyrus). In contrast, a positive quadratic age effect was reported in 5% of volumes, 6% of mean 777 thicknesses, 3% of surface areas, and a negative quadratic age effect was reported in 1% of 778 volumes, 9% of mean thicknesses, 3% of surface areas. For further details on cortical age effects, 779 see Supplemental Word Document Section 5.3. 780 Our findings coincide with and extend the literature reporting large age-related changes 781 across the cortical measures (e.g., Fjell et al., 2009; Lotze et al., 2019; Pintzka et al., 2015; Salat 782 et al., 2004; Storsve et al., 2014) The majority of frontal volumes decreased with linear age, while 783 frontal surface areas decreased with age in the orbital gyri and sulci and the inferior frontal gyrus 784 and frontal mean thicknesses decreased with age in the frontal medial and frontal superior regions. 785 Temporal surface areas and volumes generally decreased with linear age, whereas age effects on 786 temporal mean thicknesses were more variable. For instance, we observed a mean thickness 787 thinning in the lateral aspect of the superior temporal gyrus and the middle temporal gyrus and a 788 thickness increase of the planum polare, Heschl’s gyrus, lingual gyrus, and the temporal pole. 789 Occipital regions generally decreased with age in surface areas and volumes, and increased with 790 age in mean thicknesses, while parietal regions mainly decreased with age across cerebral 791 measures. 792 Our findings additionally shed a light on the inconsistent age-related changes reported in 793 motor, somatosensory, and visual cortices (Hogstrom et al., 2013; for review McGinnis et al., 794 2011). In terms of motor and somatosensory cortices, we found the largest surface area expansions 795 in the paracentral lobule and sulcus and the precentral and postcentral gyrus (motor and 796 somatosensory cortices) and a reduction of a similar size in these regions with age in terms of 797 mean thicknesses and volumes. As for the visual cortices, the largest mean thickness expansions 798 with age occurred in the cuneus gyrus, the lingual gyrus, occipital pole, the inferior, middle, and Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 33 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

799 superior, occipital gyri. The surface areas of these regions generally decreased with age and their 800 volumes were either unaffected by age or showed a slight increase with age. 801

802 803 Figure 3. Linear Age Effects across Cortical Measures. Age effects ranged from -0.40 (mean 804 thickness of the right inferior segment of the circular sulcus of the insula) to 0.22 (mean 805 thickness of the right cuneus gyrus, O6). The flat representation corresponds to the flattened 806 image of the superior view with the midline of the circle reflecting regions within the sagittal 807 plane and circle edges reflecting inferior regions. Figures made with 808 https://neuroanatomy.github.io/cortex/ (Toro, 2020).

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 34 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

809 3.3.5 Conclusion of Age Effects 810 We observed a linear change with age in 76% (480/629) and a quadratic one in 25% 811 (159/629) of regional cerebral measures. About 49% of regions decreased with linear age and 28% 812 increased with linear age. Regions showing quadratic age effects typically showed linear age 813 effects. A sex by age interaction was observed for regional measures in 14% of regions (87/629), 814 ranging from -0.16 (right cerebellar lobule X) to 0.19 (left fimbria). For detailed results on the 815 ASEG and Freesurfer subsegmentations linear and quadratic age effects, see Supplemental Info 816 5.3 and for detailed results and a discussion of the sex by age and sex by age2 interactions see 817 Supplemental Info 5.4. 818 3.4. Does Brain Allometry Influence Reported Results? 819 We examined the effects of omitting brain allometry and adjusting for TCM with different 820 methods. To do so, we compared the number of significant results from our main analyses obtained 821 with the allometric TCM adjustment to those obtained when using the linear covariate or 822 proportion TCM adjustment. The models with the linear covariate TCM adjustment yielded similar 823 significant effects and interactions (i.e., age and sex effects and their interactions with and without 824 TCM) to the allometric models: The linear covariate model under- or overestimated effects in 825 2.35% (102/4340) of statistical tests and these differences occurred in regions near significance 826 with small effect sizes (Supplemental Figures File 3 and 4, 827 https://osf.io/s4qc5/?view_only=bb067d96d0df4ae4902f99747d60e828). In contrast, the 828 proportion adjustment for TCM overestimated 14.24% (618/4340) of effects and interactions 829 reported in our main analyses compared to the allometric TCM adjustment (see Supplemental Info 830 6.2.1 and Supplemental Table F1 for details). In our replication of the FIRST subcortical and 831 Desikan-Killiany Cortical sex differences reported by Ritchie and colleagues (2018), the models 832 with the linear covariate and the allometric approach additionally yielded consistent results, except 833 for the sex differences of the left transverse temporal and the left pars opercularis volumes (β =0.02 834 for both), which only reached significance in the allometric model. Finally, based on our 835 correlational analyses of a region’s deviance from isometry (i.e., |1 - scaling coefficient|) and the 836 difference in the effect size of a term between models with varying TCM adjustments (e.g., 837 |Proportion Sex β - Allometric Sex β|), we found that discrepancies in significance between the 838 linear and allometric models were accentuated in more allometric regions, specifically for the

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 35 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

839 proportion models (see Supplemental Info 6.2.3, Supplemental Tables F5, and Supplemental 840 Figures File 5 https://osf.io/s4qc5/?view_only=bb067d96d0df4ae4902f99747d60e828). 841 Sex differences in variance differed in 38.06% (236/620) of regions between the allometric 842 and the linear covariate approach and in 29.03% (180/620) of regions between the allometric and 843 the proportion approach. These discrepancies additionally lead to a change in the direction of the 844 correlation between a region’s sex effect standardized beta and variance ratio. When adjusting for 845 TCM with the proportion or the linear covariate approach, regions that were larger in males became 846 more variable in males, instead of being more variable in females (see Supplemental Info 6.2.2 847 and Supplemental Tables F2-4). We found a similar change in the direction of the correlations 848 between the sex effect Cohen’s d and variance ratios in our replication of Ritchie and colleagues’ 849 (2018) study with the cortical Deskian-Killiany and subcortical FIRST segmentations 850 (Supplemental Table G10). 851 In line with previous research, we find more consistent results between the linear covariate 852 and allometric approach compared to the proportion and allometric approach (Mankiw et al., 2017; 853 Reardon et al., 2016; Sanchis-Segura et al., 2019). Our findings additionally suggest that the major 854 source of variation in mean results across models with differing TCM adjustments is due to the 855 omission of the intercept of the relationship between a region and its TCM (as in the proportion 856 method) rather than the omission of its non-linear relationship (as in the proportion and linear 857 covariate methods). Moreover, as the first study to examine the effects of omitting brain allometry 858 on sex differences in variance, we find that omitting brain allometry leads to over or 859 underestimating sex differences in variance depending on the region. Therefore, we suggest that 860 brain allometry generally be considered to provide unbiased estimates of age, sex, and TBV effects 861 and interactions across all brain regions, and stress that previous reported sex differences in 862 variance relative to brain size be reexamined with brain allometry (Ritchie et al., 2018; Wierenga 863 et al., n.d., 2018, 2019). 864 865 3.5 Neuroanatomical Norms 866 Neuroanatomical norms were generated for 40 028 UK Biobank participants at two levels: 867 for global brain measures (total cerebral and cerebellar GM and WM volumes, TSA, Total MCT, 868 and total subcortical and brainstem volumes) relative to TBV, and for each regional measure 869 relative to its corresponding TCM (i.e., TBV, TSA, or Total MCT). These norms correspond to

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 36 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

870 the residuals from the full statistical models and reflect the extent to which the cerebral measures 871 of an individual deviates from other individuals of the same sex, age, and total brain size. In 872 addition to creating global and regional neuroanatomical norms for each of the 629 brain measures, 873 we computed global neuroanatomical deviance markers, which reflect the deviance of an 874 individual from the norm across all brain regions. This was done separately for volumes, surfaces 875 and thicknesses, as well as across the three types of measures. 876 An individual with a “normal” brain - where all regional measures are at the expected value 877 given this individual’s sex, age, and total cerebral size - should have a global neuroanatomical 878 deviance of 0 for volume, surface and thickness. However, values ranged from 0.57 to 1.53 for 879 volumes, 0.02 to 0.05 for mean thicknesses, and 0.04 to 0.13 for surface areas, suggesting that it 880 is ‘normal’ to deviate from the cerebral norms (Table 3). In turn, individuals with a global 881 neuroanatomical deviance above the mean had brain regions that deviated from the regional norms 882 more than most individuals, while values below the mean represent reduced deviance from the 883 neuroanatomical norm. 884 The means of the volumetric, surface area, and neuroanatomical (all cerebral measures 885 combined) global neuroanatomical deviance were larger in males, suggesting that male volumes 886 and surface areas deviated more from their sex-specific norm than females. However, females 887 deviated more from their norm in the mean thickness global allometry marker. Males additionally 888 had a more variable volumetric and neuroanatomical global allometric markers (Table 3, Figure 889 4). Thus, investigations of global as well as regional neuroanatomical deviance should always take 890 sex into account. 891

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 37 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

892 Table 3. Mean and Variance Sex Differences in across Global Deviance Markers

Male Female Global Min Max d p VR p Deviance μ SD μ SD Markers for Volumes 0.57 1.53 0.85 0.96 0.82 0.92 0.27 2.20E-16 0.95 1.56E-12

Mean 0.02 0.05 0.03 0.04 0.03 0.04 0.13 2.20E-16 1.00 0.712 Thicknesses

Surface 0.04 0.13 0.07 0.01 0.07 0.01 0.12 2.20E-16 0.98 0.027 Areas

All Measures -2.14 4.74 0.05 0.74 -0.04 0.71 0.12 2.20E-16 0.97 1.12E-14 893 894 N.B. d: Cohen’s d. the Global Volumes, Mean Thicknesses, and Surface Areas Deviance Markers 895 are calculated from equation X and the Global Neuroanatomical Deviance Marker (All Measures) 896 corresponds to the average of the Z-score of the 3 Global Deviance Markers. Significance set to 897 0.05/6, as 6 tests were performed. Global volumetric deviance was positively correlated with 898 global surface area deviance (r = 0.35, p < 2.2e-16) and global mean thickness deviance (r = 0.33, 899 p < 2.2e-16). Global surface deviance and global mean thickness deviance were also positively 900 correlated (r = 0.17, p < 2.2e-16). 901

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 38 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

A) B)

C) D)

902 903 Figure 4. Sex Differences in Global Neuroanatomical Deviances across Volumes (A), Cortical 904 Surface Areas (B), Cortical Mean Thicknesses (C), and all Volumes, Cortical Surface Areas, and 905 Cortical Mean Thicknesses(D). Mean (dashed lines) differences were found across measures, 906 while variance differed between sexes only across volumes. Global Allometry marker corresponds 907 to the square root of the sum of squared residuals divided by the number of regions for that measure 908 from the model with age, total brain volume, and sex as well as age2, total brain volume, and sex 909 interactions. Global Neuroanatomical Deviance Marker corresponds to the average of the Z-score 910 of the 3 Global Deviance Markers. Significance set to 0.05/6, as 6 tests were performed. 911

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 39 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

912 With the world’s largest neuroimaging dataset, we created neuroanatomical norms in the 913 UK Biobank, to which any UK Biobank individual can be compared, in the same way that scores 914 from intelligence tests or personality questionnaires can be compared to population norms. With 915 these norms, future UK Biobank studies will be able to examine whether individuals that deviate 916 from the norm on a global or regional brain measure also deviate from the norm in terms of 917 cognitive and behavioral traits or of risk for neurological and psychiatric disorders. Having brain 918 markers that are relative to total cerebral measures (rather than raw measures) will make it easier 919 to distinguish the specific contribution of each regional brain measure from that of more global 920 brain measures. As for global neuroanatomical deviance markers, future studies will be able to 921 investigate the extent to which global neuroanatomical deviance reflects disruptions of brain 922 development or serves as a risk factor for neurodevelopmental or psychiatric disorders. For studies 923 examining the associations of specific regional brain measures with cognitive phenotypes, it may 924 be useful to adjust on global neuroanatomical deviance, on top of total brain size, in order to fully 925 dissociate regional from global effects.

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 40 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

926 3.6 Limitations 927 In light of the “healthy volunteer” selection bias and older age range of the UK Biobank 928 (Fry et al., 2017), the present paper is limited in its capacity to generalize its findings and 929 neuroanatomical norms and markers to other age groups or to the UK population. Moreover, 930 created these norms and markers are not independent of ethnicity or highest level of education 931 attained, factors thought to influence neuroanatomical measures (Shen et al., 2017; Tang et al., 932 2018). However, this enables future studies to investigate whether the present neuroanatomical 933 markers vary as a function of ethnicity and level of education. If the aim is to generalize these 934 findings to the UK population, we suggest that neuroanatomical markers be created with a 935 representative sample or that weights be used to adjust the phenotypic measures of the UK Biobank 936 to match those of the UK population. 937 While numerous studies focus on developing machine learning algorithms (e.g., SVM 938 classifications) to generate neuroanatomical markers, we were interested in identifying sex, age, 939 and TCM effects while considering their potential interactions, which are often omitted in the 940 literature. By opting for a regression approach, we were able to quantify effects and interactions 941 for each region, which would have been lost with machine learning. Future studies would 942 nevertheless benefit from examining the age, sex, and global brain effects of other anatomical 943 measures, such as diffusion tractography, and functional measures in the UK Biobank. 944 While the present study modelled age as a linear and quadratic function, other studies 945 examining sex and age interactions used the nonparametric local smoothing technique (i.e., 946 smoothing splines; Fjell et al., 2013; Vinke et al., 2018), which are thought to be more predictive 947 of individual trajectories and less vulnerable to sampling range (Fjell & Walhovd, 2010). However, 948 this nonparametric approach also requires researchers to make more decisions that contribute to 949 the variability of results. For instance, Fjell and colleagues (2010) initially selected the spline 950 smoothing level that minimized the AIC, but when the absence of smoothing (which is equivalent 951 to the linear least square model) yielded the smallest AIC for the sample of individuals over 60 952 years old, they chose the smoothing level that minimized the BIC. Considering that the 953 nonparametric local smoothing technique depends on selected parameters and that splines are 954 difficult to interpret if we are interested in quantifying the magnitude of age effects, quadratic age 955 was used instead of splines to model non-linear age in the present study.

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 41 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

956 4. Conclusion

957 The present study is the largest analysis to date of the age, sex, and TCM effects and 958 interactions on global and regional brain volumes, cortical mean thicknesses, and cortical surface 959 areas. We provide further evidence that brain allometry is a common property of the brain that 960 should be considered to report unbiased estimates of age, sex, and TCM effects and interactions. 961 By generating volumetric and allometric norms in the UK Biobank, we pave the way for future 962 research to examine the associations between these markers and the behavioral and cognitive traits 963 available in the UK Biobank. Once associations between these UK Biobank neuroanatomical 964 norms and cognitive and behavioral measures are established, researchers will be able to examine 965 the extent to which these neuroanatomical markers mediate the effect that genes and the 966 environment have on these traits. This line of research will play critical role in our understanding 967 of the influence that neuroanatomy has on who we are. 968

Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 42 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

969 5. References

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Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 43 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 45 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 47 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 48 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV). bioRxiv preprint doi: https://doi.org/10.1101/2020.12.14.422684; this version posted December 15, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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Abbreviations: Total Cerebral Measures (TCMs): Total Brain Volume (TBV), Total Mean 55 Cortical Thickness (MCT), or Total Surface Area (TSA). Grey Matter Volume (GMV). White Matter Volume (WMV).